Algebra I: word problem?

Kendra earned $192 from the sale of flower arrangements that she had made. IF she charged $8 more apiece, she could have sold two fewer arrangements and still have earned the same amount. How many arrangements did Kendra sell?



Can you help me solve this?

Algebra I: word problem?
Let x be the number of arrangements she sold. So she charged 192/x for each of them.



IF... she'd charged (192/x)+8 for them instead, she would have sold x-2 of them and still made 192 dollars. This can be represented by this equation:



[(192/x)+8] * (x-2) = 192

Let's play around with this a bit.

[(192+8x)/x] * (x-2) = 192

Multiply left- and right-hand sides by x:

(192+8x) * (x-2) = 192x

(8x+192) * (x-2) = 192x

8x2 + 176x - 384 = 192x

8x2 + 176x - 192x - 384 = 0

8x2 - 16x - 384 = 0

Divide both sides by 8:

x2 - 2x - 48 = 0

Factorise:

(x-8)(x+6) = 0

x-8 = 0 or x+6 = 0

x = 8 or x = -6



Obviously Kendra can't sell -6 arrangements, so the answer is 8.



To back this up: she sold 8 arrangements and got $192, so she sold them for $24 each. "IF she charged $8 more apiece [$32 apiece], she could have sold two fewer arrangements [6] and still have earned the same amount." $32 multiplied by 6 equals... $192, so the algebra was right.



How many arrangements did Kendra sell? Eight.
Reply:Thank you for choosing me!!! Report It
Reply:Let n be the number of arrangements sold, and p is the price. We are told that n*p = 192. But we are also told

(n - 2) * (p + 8) = 192

So you have two equations here. Solve the first for "p":

n*p = 192

p = 192/n

And substitute this into the second equation

(n - 2) * (p + 8) = 192

(n - 2) * [(192/n) + 8) = 192

Multiply both sides by "n" to clear the fraction:

(n - 2) * (192 + 8n) = 192n

192n + 8n^2 - 384 - 16n = 192n

8n^2 - 16n - 384 = 0

n^2 - 2n - 48 = 0

(n - 8)(n + 6) = 0

n = 8 or n = -6

Since n (the number of arrangements sold) cannot be negative, n must be 8.



So she sold 8 arrangements at $24 each. Had she sold 6 arrangements at $32 each, she would have made the same amount of money.
Reply:let x= no. of arrangement

kenda----.192-------%26gt; from x

x-2-------8(x-2)=192

8X-16=192

8x=208

x=26 therefore 26 arrangements